Answer: The correct option is (B) [tex]\sqrt{205}.[/tex]
Step-by-step explanation: We are given to find the length of the segment whose endpoints are A(-4, 3) and B (10, 6).
We know that
the length of a line segment with endpoints (a, b) and (c, d) is calculated using distance formula as follows :
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, using distance formula, the distance between the endpoints A(-4, 3) and B (10, 6) is given by
[tex]AB\\\\=\sqrt{(10-(-4))^2+(6-3)^2}\\\\=\sqrt{(10+4)^2+3^2}\\\\=\sqrt{14^2+9}\\\\=\sqrt{196+9}\\\\=\sqrt{205}.[/tex]
Thus, the length of the line segment AB is [tex]\sqrt{205}~\textup{units}.[/tex]
Option (B) is CORRECT.
